You actually bring up the exact difference in notion of Japanese terms in Japan vs US.

"Cosplay" is a Japanese term abbreviating "costume" + "play" -- So essentially playing a role through dressing in costume.
So in Japan, wearing any costume would count as cosplay.
Whereas, if you ask some people in the US, they might be purists and think it has to be an anime/manga costume.

UNY Cosplay has always been very accepting of costumes of any origin -- Even original costumes!

Similarly, Anime is the Japanese term abbreviating "animation" -- So technically cartoons count as anime... But if you tell some people that in the US, they would say "NO IT"S COMPLETELY DIFFERENT!". So whaddya know.

And once again -- "otaku". Americans have come to use otaku to mean someone who's obsessed with Anime/Video Games, but used in Japan, otaku can mean any kind of obsession. There are train otaku, war otaku, and movie otaku, for example.

Well, I think if you're wearing a maid outfit, say, you're certainly cosplaying; you may not be anyone specific, but it's still a costume. One could also point out the prevelance of Darth Vaders and the like at "mostly anime" cons.